Transcript Circular & Satellite Motion

Circular & Satellite Motion
Physics I
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Types of Speed
• Linear speed is the distance traveled per unit of time.
• The speed of something moving along a circular path can be
called tangential speed because the direction of motion is
always tangent to the circle.
•Rotational speed (sometimes called angular speed) is the
number of rotations (or revolutions) per unit of time. All parts
of the rigid turntable rotate about the axis in the same amount
of time
Ask your parents about Record players
and what speeds they played? Come to
class with the answer.
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All parts of the turntable rotate at
the same rotational speed.
a. A point farther away from the
center travels a longer path in
the same time and therefore has
a greater tangential speed.
b. A ladybug sitting twice as far
from the center moves twice as
fast.
Lady Bug Revolution - Phet
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Uniform Circular Motion
An object moves at a
constant speed in a circle:
Uniform circular motion is motion
along a circular path in which
there is no change in speed, only
a change in direction.
d 2r
v 
t
T
1
T
f
T = Period (seconds)
f = Frequency (Hertz)
v = Tangential or linear velocity
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Examples of Period
1. 10 sec/1 lap = 10 sec
2. 10 sec/ 2 laps = 5 sec
Examples of Frequency
1. 10 laps/5 sec
2. 10 laps/ 20 sec
Notice the difference
between period and
frequency.
What is the period of
one lap if 10 laps
were covered in 20
seconds? What did
you do?
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Suppose that a mass, m, is tied to the end of a
string and is being whirled in a horizontal circle as
shown in the diagram.
What is causing the mass to move in a circle?
Why is it considered to be accelerating?
Top View:
v2
ac 
r
“center seeking”
Centripetal Acceleration:
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Centripetal Force vs. Centrifugal force??
Centripetal Force – a NET force toward the center
Centrifugal Force – an imaginative force an object
experiences due to Newton’s first Law of Motion
(Inertia).
The feel of being pushed out, when
instead being pulled in while trying to
continue to move in a straight line.
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If the string breaks, in which direction will the object fly?
a
vo
vf
Tangent to the circle.
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Centripetal Force, Fc
Fc
Circular Motion Applet
mv
Fc  mac 
r
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If a friend is driving the car and makes a hard turn
to the right, in which direction do you move if you
are in the front passenger’s seat? Why?
What forces are acting on you and in what
direction?
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Sharp Turn in Car
Why do we hit the door?
The centripetal force
is exerted BY the
door ON you.
(Centrally)
What is the force from the door acting on the rider called?
The Normal Force
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Author: Tippens, P. (2007)
Without a centripetal
force, an object in
motion continues
along a straight-line
path.
With a centripetal force,
an object in motion will
be accelerated and
change its direction.
thephysicsclassroom.com
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Example 1: A skater moves with 15 m/s in a
circle of radius 30 m. The ice exerts a central
force of 250 N. What is the mass of the skater?
Draw and label sketch
Solution:
v = 15 m/s
Fc
250 N
R
30 m
m=?
Speed skater
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Author: Tippens, P. (2007)
Hills & Loops
The Physicsclassroom.com
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Platform Ride – You Tube (External View)
Platform Ride – You Tube (Internal view)
Another Example
Disappearing
platform at fair.
R
Fc
What exerts the centripetal force in this example
and on what does it act?
The normal force from the wall acts
as the centripetal force. Friction
holds the person up.
Normal
Force
Friction
Weight
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Author: Tippens, P. (2007)
Spin Cycle on a Washer
How is the water removed from
clothes during the spin cycle of a
washer?
Think carefully before answering . . . Does the centripetal
force throw water off the clothes?
The holes in the drum allow water to “fly” off because of inertia.
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Author: Tippens, P. (2007)
The Effect of speed on Centripetal Force
The model airplane has a mass of 0.90 kg and moves at a
constant speed on a circle that is parallel to the ground.
Find the Tension in the guideline (17 m) for speeds 19
m/s and 38 m/s.
What is counteracting
gravity if it is flying
parallel to the ground?
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Friction and a Car on a Curved Road
FFNN
If Fc  Ff, then the
car will make the
curve
Ff
Fg
Record player demo- Double coins
If Fc > Ff, then the
car will not make
the curve.
Critical Point:
Fc = Ff
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Vertical Circles
In a vertical circle, if Fg is greater than the Fc required to
keep the object in a circle, then the object will fall. The
critical point is when Fg = Fc. This is used to determine
the minimum or maximum speed at which an object can
move and stay in the circle.
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Circular Motion Practice Problem
1. A coin is placed on a record player at a radius of 15 cm from
the center. The rotational speed is set to 45 rpms.
a.What is the period of one revolution?
b.
What is the linear speed of the coin?
c.
How will placing an additional identical coin top of the
existing coin affect the centripetal force?
d. Recall from earlier demonstrations and lectures: Will adding
the extra coin affect whether they will slip off the turntable?
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Practice Problems
1. A 1000 kg car completes two revolutions in 1 minute on
a circular track with a 1 km radius.
A. What is the period of one revolution?
B. What is the car’s linear speed?
C. What is the centripetal force acting on the car?
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Your Turn!
2. A 5 kg mass is traveling a 6 m/s in a horizontal circle
with a 60 cm radius.
a. What is the centripetal acceleration?
Ac = 60 m/s2
b. What is the centripetal force?
Fc = 300 N
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Newton’s Law of Universal Gravitation
Newton discovered that gravity is universal.
Everything pulls on everything else in a way that
involves only mass and distance.
Gm1m2
F
r2
Universal Gravitation Constant:
G = 6.67x10-11 Nm2/kg2
m1
F
F´
m2
r
F = -F´
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Cavendish Experiment
English physicist, Henry Cavendish determined G by
measuring the tiny force between lead masses with an extremely
sensitive torsion balance.
g=?
Force of Attraction = Weight
Gm1m2
F
 m1 g
2
r
m1
Weight
m2
Gm2
g
2
r
Mass of Earth = 5.98 x 1024 kg
Radius of Earth = 6.37x106 m
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Graviational Strength vs. Radial
Distance
1.2
Graviational Strength
1
0.8
0.6
0.4
0.2
0
1
Inverse Square
Relationship
2
3
Distance (Re)
4
5
1
F 2
r
If r = 3RE, what would be your weight?
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Relationship Examples
1. If the radial distance doubles, then the force of
attraction between 2 masses
_________________.
2. If your weight dropped by a factor of 1/16th , then you
must be ____ RE away.
3. If one mass doubled then the force of attraction
_____________.
4. If one mass increased by a factor of 2 and the other
mass decreased by a factor of 4, then the force of
attraction would be _________________ .
5. The force of attraction is F. If the radius increased by a
factor of 5, the new force would be ______.
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Universal Gravitation - Sample Problems
1. A space capsule weighs 500 N on the surface of the earth.
How much does the capsule weigh when it is 4.50 x 108 m
above the surface of the earth?
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2. A force of 1.2x10-13 N exists between a 30 g
mass and an unknown mass. Calculate the
second mass if they are 1 m apart.
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Your Turn!
3. What is the force of attraction between a 5000g object and a
4000 g object when 30 cm apart? (Don’t forget to convert!!)
Ans: 1.48x10-8 N
Pause for
Practice
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Newton & Falling Apple
Is the Moon Falling?
Hewitt, P. [Illustrations]. Conceptual Physics.
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Elliptical Orbits
Newton’s Mountain Animation
Hewitt, P. [Illustrations]. Conceptual Physics.
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Satellite Orbit
In order for the satellite to orbit the Earth in a
circle, the gravitational force is also the
Centripetal force
_______________________.
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Apparent Weight is zero in orbit because of free-fall but the
true weight is determined by Newton’s Law of Universal
Gravitation.
Satellite Orbit
If the satellite is in free fall, why does it not come crashing
into the Earth?
Zero Gravity
with water:
http://www.youtube.com/watch?v=r7fEHYkGxd0&feature=related
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Kepler’s Laws of Planetary Motion
1. The paths of the planets are
ellipses with the center of the sun at
one focus.
2. An imaginary line from the sun to a
planet sweeps out equal areas in
equal time intervals. Thus the planets
move fastest when closest to the sun,
slowest when farthest away.
3.
2
 T1   r1 
    
 T2   r2 
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Kepler’s Laws Animation
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Universal Gravitation – Practice Problems
1.Two identical masses experience a force of 100 N when placed
20 cm apart. What is the mass of each?
2.A 5.8x106 kg mass and a 6.4x 105 kg mass experience an
attracting force of 2.47x10-4 N. How far apart are the masses?
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Bellringer Questions
You have 5 minutes to answer the following questions individually.
1. If you weighed 1/16th of your current weight, then you would be located __
Earth radii away.
A. 1
B. 2
C. 4
D. 8
2.
What is the force of attraction between a 20 kg and a 50 kg object located 2
m apart? 1.6x10-8 m
3. ___ measured the constant G.
A. Galileo
B. Newton
4.
C. Cavendish
Linear Review Wkst Page 4
The relationship on the curve is
A. Linear
B. Quadratic
C. Inverse
5. Linear Review Wkst Page 4:
If a coin and a feather were dropped in a vacuum at the same time, they
would have the same
A. speed
B. Acceleration C. Resistance
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Bellringer Questions
You have 5 minutes to answer the following questions individually.
1.
A mass travels at 2 m/s in a circle with a radius of 0.9 m. What is the
centripetal acceleration? 4.44 m/s2
2.
Linear Review Wkst Page 3:
What is the instantaneous speed of an object that is at its highest point
when it is thrown straight up in the air?
A. 9.8
B. 0
C. 4.9
3.
Linear Review Wkst Page 3
When an object is in free fall, it falls a(n) ____ distance with each second.
A. Lesser
B. greater
C. equal
4.
Linear Review Wkst Page 3
What is the slope of the graph represent?
acceleration
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Bellringer Questions
You have 5 minutes to answer the following questions individually.
1. If you weighed 1/16th of your current weight, then you would be located __
Earth radii away.
A. 1
B. 2
C. 4
D. 8
2.
What is the force of attraction between a 20 kg and a 50 kg object located 2
m apart?
3. ___ measured the constant G.
A. Galileo
B. Newton
C. Cavendish
4.
The relationship on the curve is
A. Linear
B. Quadratic
C. Inverse
5.
If a coin and a feather were dropped in a vacuum at the same time, they
would have the same
A. speed
B. Acceleration C. Resistance
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Credits:
Cutnell & Johnson Physics. (2004). [Text Art CD]. John Wiley & Sons.
Cartoon (Author Unknown). Received from 2007 AP Conference Complimentary
Resource CD.
Hewitt, P. [Illustrations]. Conceptual Physics.
Hwang. F. (200). Circular Motion & Centripetal Acceleration Applet [Simulation].
Retrieved from
http://www.phy.ntnu.edu.tw/oldjava/circularMotion/circular3D_e.html
Tippens, P. (2007). Chapter 10 Uniform Circular Motion. [PowerPoint Slides].
Received from 2007 AP Conference Complimentary Resource CD.
The Physics Classroom. [Animations]. http://www.thephysicsclassroom.com
UC Irvine Physics of Music. (n.d.). Simple Harmonic Motion [Simulation]. Retrieved
from http://positron.ps.uci.edu/~dkirkby/music/html/demos/SimpleHarmonic
Motion/index.html
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Demo
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A student is standing on a merry-go-round
that is rotating counterclockwise, as
illustrated above. The student is given a
ball and told to release it in such a way
that it knocks over the wicket at the top of
the diagram. At what point should the
student release the ball?
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